Trigonometry (Right Triangles)
Overview
Trigonometry in a right triangle starts with three ratios — sine, cosine, and tangent — each comparing two sides relative to a chosen reference angle. This lesson names the sides (hypotenuse, opposite, adjacent) from the reference angle's point of view, writes the ratios with the SohCahToa mnemonic, evaluates ratios from side lengths, and uses the ratios to find missing sides. Before any calculation, confirm the calculator is in degree mode: sin 30° must return 0.5.
Vocabulary
- Trigonometric Ratio
- A ratio of the lengths of two sides of a right triangle, written relative to a reference angle.
- Reference Angle
- The angle a trigonometric ratio refers to. The right angle is never used as a reference angle.
- Hypotenuse
- The side opposite the right angle — always the longest side of the right triangle.
- Opposite Side
- The side directly across the triangle from the reference angle.
- Adjacent Side
- The side next to the reference angle that is not the hypotenuse.
- Sine, Cosine, Tangent
- For a reference angle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. The mnemonic SohCahToa helps you remember them.
Main Ideas
- "Opposite" and "adjacent" depend on which angle is the reference angle; the hypotenuse never changes.
- SohCahToa: Sin = Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj.
- To find a missing side, choose the ratio that involves the known side, the side you want, and the reference angle — then solve the equation.
- Watch the setup before the arithmetic: if the unknown side is in the denominator, multiply both sides to clear it rather than dividing by the ratio.
- Round final answers as directed (for example, to the nearest tenth), and keep full precision until the last step.
Lesson Notes
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Lesson Video
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Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.